Electrical conversion

Decibel (dB) conversion

Convert power and amplitude ratios to decibels. Power: dB = 10·log₁₀(P₂/P₁). Amplitude/voltage: dB = 20·log₁₀(V₂/V₁). Runs locally in your browser.

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Formulas

Core equations used by this converter.

Power ratioL(dB) = 10 × log₁₀(P₂/P₁)

Amplitude ratioL(dB) = 20 × log₁₀(A₂/A₁)

iUse equal impedances when interpreting a voltage level difference as a power difference. A ratio of 1 gives 0 dB.

How to use

Choose Power ratio or Amplitude ratio

Choose the quantity measured before forming the ratio.

Enter the positive ratio

Divide the two values expressed in the same unit before entering the ratio.

Read the level difference

Ratios above 1 give positive dB and ratios below 1 give negative dB.

Example conversions

Common values with formula and result.

Power doubles

10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB

Power ×10

10 × log₁₀(10) = 10 dB

10 dB

Voltage doubles (same Z)

20 × log₁₀(2) ≈ 6.02 dB ≈ +6 dB

Half power (−3 dB)

10 × log₁₀(0.5) ≈ −3.01 dB

Decibel (dB) conversion specification

Version 1.1.1 · Engine tested

Calculation status

Engine tested 4 published cases
Named expert review Not performed
Calculation version 1.1.1

Review policy

Definition: A decibel expresses a logarithmic level difference. Choose the power or amplitude formula for a positive ratio of two quantities of the same kind.
What it calculates: Convert power and amplitude ratios to decibels. Power: dB = 10·log₁₀(P₂/P₁). Amplitude/voltage: dB = 20·log₁₀(V₂/V₁). Steps, examples, and FAQ.
Inputs: Positive dimensionless power ratio or amplitude ratio
Outputs: Level difference (dB)
Formula: L(dB) = 10 × log₁₀(P₂/P₁) or L(dB) = 20 × log₁₀(A₂/A₁)
db converter chart: Ratio Power dB Voltage dB
×0.5 ≈ −3 dB ≈ −6 dB
×1 0 dB 0 dB
×2 ≈ +3 dB ≈ +6 dB
×10 +10 dB +20 dB
×100 +20 dB +40 dB
Assumptions: Conversion runs locally in the browser; values are not uploaded.
The numerator and reference represent the same quantity and use the same unit.
Units: Dimensionless ratio
dB
Boundary conditions: Empty or invalid input yields no valid result.
Zero and negative ratios are outside the logarithm domain.
Example: Power doubles → 10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB
Validation cases: Power doubles → 10 × log₁₀(2) ≈ 3.01 dB ≈ +3 dB
Power ×10 → 10 dB
Voltage doubles (same Z) → 20 × log₁₀(2) ≈ 6.02 dB ≈ +6 dB
Half power (−3 dB) → 10 × log₁₀(0.5) ≈ −3.01 dB
Sources: NIST Guide to the SI, Section 8.7 (https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8)
CalculatorX UUCE ratio definition, snapshot 0.3.0-preview.3
Calculation version: 1.1.1

Ratio	Power dB	Voltage dB
×0.5	≈ −3 dB	≈ −6 dB
×1	0 dB	0 dB
×2	≈ +3 dB	≈ +6 dB
×10	+10 dB	+20 dB
×100	+20 dB	+40 dB

Background

Interpretation and common distinctions.

Use the tabs to choose a power or amplitude ratio. The level difference updates locally in your browser.

Frequently asked questions

Key distinctions behind the conversion.

How do I convert a ratio to decibels?

A power ratio of 2 gives approximately 3.010300 dB. An amplitude ratio of 2 gives approximately 6.020600 dB.

Why are there two modes?

Use the power mode for a power ratio and the amplitude mode for a ratio of amplitudes, such as voltage.

Does this run online or locally?

Calculation runs locally in your browser. Values are not uploaded.

How precise are the results?

Results follow the formulas on this page. Round to the precision your use case needs.